Critical thickness for the Stranski-Krastanov transition treated with the effect of segregation

Abstract

A new estimation of the critical thickness for the 2D–3D transition during epitaxial growth of the Ge x Si1 − x /Si(001) and In x Ga1 − x As/GaAs(001) systems is suggested. In the estimation, the segregation of atoms in the process of growth is taken into account. For the criterion of such a Stranski-Krastanov transition, the balance between the gain in the energy of elastic strains in the system due to relaxation of the island and the loss in surface energy because of the increase in the surface area is used. In contrast to calculations for previously known criteria, the energy of elastic strains is calculated taking into consideration all deposited layers rather than only one upper layer. The segregation is described in the model of thermally activated exchange of atoms between the surface and the upper layer. A comparison of the critical thickness, calculated for different compositions of the deposited alloy at different temperatures and rates of growth, with the experimental data shows rather good agreement for both systems. The transition mechanisms corresponding to the criterion suggested in the study are discussed.